Introduction

Dynamics follows kinematics. Kinematics tells you where things are and how fast they are moving; dynamics tells you what forces and torques are needed to get that motion to happen (or, run the other way, what motion results from given forces/torques). Kinematics deliberately ignores mass and force but dynamics is built around modelling these physical quantities.

In practice, most robotics projects do not require full dynamics modeling. Dynamics starts to matter when we need precise, fast, or heavily-loaded motion (such as in industrial arms or legged robots), or if we require simulation of a robot while adhering to physical principles.

Key Concepts

• Equation of motion — an equation relating joint torques to joint positions, velocities, and accelerations. Usually written as:

$$ \tau = M(q)\ddot{q} + C(q,\dot{q})\dot{q} + G(q) $$

where $M$ is the mass/inertia matrix, $C$ captures Coriolis/centrifugal effects, and $G$ is the gravity term.

• Forward vs. Inverse Dynamics —

Inverse dynamics: given desired motion, compute the torques needed (used for control).

Forward dynamics: given applied torques, compute the resulting motion (used for simulation).

• Newton-Euler vs. Lagrangian formulation — There are two standard ways to derive the equations of motion. Newton-Euler is a recursive, link-by-link force/torque balance (used in simulators). Lagrangian is an energy-based approach (kinetic minus potential energy) that's more compact.

Applications in Robotics

• Feedforward/computed-torque control on arms that need precision or speed beyond standard control methods
• Physics simulation (Gazebo, MuJoCo, PyBullet): forward dynamics is what actually steps the simulation forward each frame
• Legged robot balance and locomotion

Resources

Repos

• NxRLab/ModernRobotics

Courses / Videos